The effect of explicit convection on simulated malaria transmission across Africa

Malaria transmission across sub-Saharan Africa is sensitive to rainfall and temperature. Whilst different malaria modelling techniques and climate simulations have been used to predict malaria transmission risk, most of these studies use coarse-resolution climate models. In these models convection, atmospheric vertical motion driven by instability gradients and responsible for heavy rainfall, is parameterised. Over the past decade enhanced computational capabilities have enabled the simulation of high-resolution continental-scale climates with an explicit representation of convection. In this study we use two malaria models, the Liverpool Malaria Model (LMM) and Vector-Borne Disease Community Model of the International Centre for Theoretical Physics (VECTRI), to investigate the effect of explicitly representing convection on simulated malaria transmission. The concluded impact of explicitly representing convection on simulated malaria transmission depends on the chosen malaria model and local climatic conditions. For instance, in the East African highlands, cooler temperatures when explicitly representing convection decreases LMM-predicted malaria transmission risk by approximately 55%, but has a negligible effect in VECTRI simulations. Even though explicitly representing convection improves rainfall characteristics, concluding that explicit convection improves simulated malaria transmission depends on the chosen metric and malaria model. For example, whilst we conclude improvements of 45% and 23% in root mean squared differences of the annual-mean reproduction number and entomological inoculation rate for VECTRI and the LMM respectively, bias-correcting mean climate conditions minimises these improvements. The projected impact of anthropogenic climate change on malaria incidence is also sensitive to the chosen malaria model and representation of convection. The LMM is relatively insensitive to future changes in precipitation intensity, whilst VECTRI predicts increased risk across the Sahel due to enhanced rainfall. We postulate that VECTRI’s enhanced sensitivity to precipitation changes compared to the LMM is due to the inclusion of surface hydrology. Future research should continue assessing the effect of high-resolution climate modelling in impact-based forecasting.

For a compartmental infectious disease model, an expression for the basic reproduction number, R 0 as a function of model parameters is determined by considering the steady-state conditions of the governing differential equations.R 0 therefore gives an indication of the suitability of conditions, as described by the model parameters, for sustained or increasing disease transmission.For LMM, R 0 is given by equation 1 [1]: where the biting rate (a; day −1 ); mosquito mortality (µ; 0 to 1); sporogonic cycle length (τ y ; days); and vector density (m), are all climate-dependent variables and calculated using daily-mean temperatures (T ; • C) and daily-accumulated rainfall (R; mm day −1 ) (equations 2-5).b, c, r and τ x are prescribed climate-independent parameters representing, respectively: the human and mosquito inoculation efficiencies, the human recovery rate (day −1 ), and the time in humans between infection and infectiousness (the latent period; days).Table S1 shows the prescribed values used for climate-independent model parameters.These prescribed values are taken from [2] and altered for this simplified version of the LMM.The daily vector density, i.e. the number of adult mosquitoes, is proportional to 10-day rainfall accumulations: where subscript i represents the daily value and n determines the number of days which precipitation is accumulated over (10).The probability of mosquito survival (µ) also impacts the number of adult mosquitoes and is based on a quadratic relationship given with temperature [3]: a and τ y depend on temperature and are formulated using: where HBI denotes the human blood index (dimensionless); T g denotes the gonotropic temperature threshold (  Further details about the model parameterisation can be found in [5].The VECTRI source code and documentation can be found at http://users.ictp.it/∼tompkins/vectri/.

S2 Determining the best set of observational climate products
Here we investigate the best combination of precipitation and temperature observations to drive historical malaria simulations.To do this we compare LMM output from nine experiments driven with different precipitation and temperature datasets (Table S2) with estimates of malaria endemicity from MAP (section 2.2).Due to both the LMM and VECTRI requiring precipitation and temperature at a daily temporal resolution, we were limited in our choice of pan-African observational datasets.For our nine LMM experiments we vary between three temperature products: the European Centre for Medium-Range Weather Forecasts (ECWMF) Reanalysis version 5 (ERA5) [6; 7]; Berkeley Earth Surface Temperatures (BEST) [8]; and temperatures from phase 2b of the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP2b) [9], and three precipitation products: ERA5; the Climate Hazards group InfraRed Precipitation with Stations (CHIRPS) [10]; and ISIMIP2b.A description of ERA5 and CHIRPS is provided in the methodology section (section 2.3.1).BEST data uses long-term in situ station data records to output daily temperatures on a 1 • latitude/longitude grid.Temperature observations are interpolated onto the horizontal grid using Kriging [11], also known as Gaussian Process Regression, which is the best linear unbiased predictor of the underlying field [8].Meanwhile, data sources for ISIMIP2b include ERA-Interim reanalysis (ERAI) [12], a WATCH (Water and Global Change) forcing data methodology applied to ERAI data (WFDEI) [13], eartH2Observe forcing data (E2OBS) [14], and NASA/GEWEX (National Aeronautics and Space Administration/Global Energy and Water Exchanges) Surface Radiation Budget data (SRB) [15].Temperature and precipitation data for ISIMIP2b is outputted on a 0. impact-based modelling across a variety of sectors including agriculture, water quality and health.In particular for phase 2b, the project aimed to assess the impacts of an anthropogenic global-mean temperature rise of 1.5 • C [9].All datasets have been remapped onto the same 0.25 • latitude/longitude grid as R25 simulations (section 2.3.2) using a first-order conservative interpolation scheme [16].
Table S2 shows the simulation name given to each LMM experiment driven with different climate observational data.The labelling of all experiments follows the same structure with the source of precipitation (P) data followed by the source of temperature (T) observations.We use "E5", "B", "IS" and "Ch" as shorthand to denote ERA5, BEST, ISIMIP and CHIRPS datasets respectively.Figure S1 shows the annual-mean number of days when R 0 is greater than 1.0 in all LMM experiments driven with different observational datasets.In general, all LMM experiments simulate high malaria risk across the Guinea coast, central Africa and coastal regions of south-east Africa.There are substantial differences in predicted malaria risk across parts of equatorial Africa when changing the driving temperature dataset.For example, using temperatures from BEST predicts a much smaller malaria risk across central Africa compared to when using ERA5 or ISIMIP regardless of the chosen precipitation product.Whilst varying the driving temperature dataset leads to substantial differences in LMM-predicted malaria risk, we also conclude that varying the precipitation product can impact simulated malaria incidence.For example, when using precipitation from ISIMIP, simulated malaria risk across coastal regions of western central Africa are much larger compared to when using CHIRPS or ERA5.
To conclude which combination of precipitation and temperature data is best to drive our "observed" malaria simulation experiments, we compute the spatial correlation between the simulated annual-mean number of days when R 0 is greater 1.0 and the estimated Pf incidence rate from MAP. Spatial correlation coefficients between LMM experiments vary between 0.19 to 0.45 (Fig S1).Unsurprisingly, using precipitation from ERA5 has the lowest agreement with MAP-derived incidence rate as ERA5 precipitation relies on parameterisations of deep convection.Spatial correlations improve when using precipitation from EWEMBI due to bias-correcting reanalysis data and the merging of several hydrological products [17].Using precipitation data from CHIRPS simulates the largest spatial correlations with MAP data regardless of the chosen temperature product.Given that MAP data is partly derived using in situ station and satellite-derived environmental data (section 2.2), it is unsurprising that CHIRPS is the best precipitation product to use.Previous studies have also shown that CHIRPS is one of the most reliable pan-African precipitation products available [10; 18; 19].However, when considering the best temperature product, temperatures from ERA5 give the largest correlation coefficients regardless of the chosen precipitation dataset.Using temperatures from BEST gives the lowest agreement with MAP estimates which we hypothesise is due to the low number of temperature observations across equatorial Africa [20].Using temperatures from ISIMIP instead of BEST increases spatial correlations, whilst temperatures from ERA5 increases correlations even further.Higher spatial correlations when using temperatures from ERA5 is unsurprising given it is the only temperature dataset originally produced at a 0.25 • horizontal resolution.Given that the combination of CHIRPS precipitation and ERA5 temperatures produces the largest spatial correlation coefficient, for the rest of the study we treat malaria experiments driven with these two datasets as our "observational" malaria experiment.

S3 Simulated temperature and precipitation biases
In this supplementary section we assess the ability of CP4 h and R25 h at simulating historical precipitation and temperature.Given that we conclude that temperatures and Figure S3a shows the fractional contribution of all daily precipitation rates across land points south of 20 • N. We find a larger fraction of days with light precipitation (≤ 10 mm day −1 ) in R25 h compared to CP4 h .However, CP4 h overestimates the fraction of days when precipitation is greater than approximately 20 mm day −1 to a greater degree than R25 h .Therefore, we conclude that larger biases in 10-day precipitation accumulations in CP4 h compared to R25 h (Fig S2i) are associated with too many heavy rainfall days.CP4 h has a strong negative temperature bias across the Sahel (Fig S2j).Decomposing annual-mean errors into seasonal contributions highlights that similar errors are found across the Sahel during dry seasons.From July to September, the wet season associated with the West African monsoon, near-surface temperature biases are minimum (not shown).Given that temperature errors across the Sahel are largest during dry seasons, and that malaria transmission is favoured during wet conditions (section 2.1), we also investigate wet-day temperature biases (Fig S2m-o).In general, CP4 h has larger wet-day temperature errors with the RMSD being 0.18 • C greater in comparison with R25 h .The difference in wet-day temperatures between CP4 h and R25 h highlights that temperatures are consistently cooler in CP4 h when it is raining (Fig S2o).Cooler wet-day temperatures in CP4 h compared to R25 h is seen across all seasons (not shown).This is consistent with findings by [22] who conclude that higher cloud tops in CP4 h leads to a greater reflection of incoming shortwave radiation and reduced near-surface heating.Figure S3b shows the fractional contribution of temperatures across all land grid points.Consistent with aforementioned results (Fig S2j -o), CP4 h favours cooler near-surface temperatures than R25.Outside of approximately 21 to 29 • C, R25 h is more consistent with observations compared to CP4 h .This indicates that R25 better resolves the frequency of high near-surface temperatures (≥ 29 • C).To summarise, whilst the rainfall frequency and daily-mean precipitation rate is better resolved in CP4 h compared to R25 h , larger errors in 10-day precipitation accumulations and near-surface temperatures are found in CP4 h .In this study, we investigate the impact of cooler wet-day temperatures and higher 10-day January 17, 2024 4/8 rainfall accumulations in CP4 h compared to R25 h on simulated malaria transmission.

S4 Supplementary figures
Fig S1 .Annual-mean number of days when R 0 is greater 1.0 from LMM experiments driven with different observational products.First, second and third rows are driven with ERA5, CHIRPS and ISIMIP precipitation respectively.Whilst first, second and third columns are driven with ERA5, BEST and ISIMIP temperature.In all panels boxed values note the spatial correlation coefficient between the annual-mean number of days when R 0 is greater 1.0 and MAP data (Fig 1a).To ensure that the spatial correlation is not biased towards regions of low malaria incidence, we remove all grid points where the MAP-derived Pf incidence rate is smaller than 0.1.We also removed grid points where the simulated annual-mean number of days when R 0 is greater than 1.0 is outside the range of 15.0 and 140.0.To be consistent with the time span of available MAP data [23], we only compare malaria model output which is driven with climate model data from years 2000 to 2007.All correlations are statistically significant at a 99% confidence interval.Land and country boundaries were added using Natural Earth; free vector and raster map data available at naturalearthdata.com.

Fig S2 .
Fig S2.Annual-mean differences in (a-c) 10-day precipitation accumulations (mm), (d-f) the number of wet days (≥ 1 mm), (g-i) mean wet-day precipitation rate (mm), (j-l) daily-mean near-surface air temperature ( • C), and (m-o) daily-mean wet-day near-surface air temperature ( • C).Differences are shown between (first column) CP4 h and observations, (second column) R25 h and observations, and (third column) CP4 h and R25 h .Values above each panel label, document the root mean squared difference (RMSD) across land points south of 20 • N in each panel.Land and country boundaries were added using Natural Earth; free vector and raster map data available at naturalearthdata.com.

Table S1 .
Parameter values used for LMM simulations

Table S2 .
LMM malaria transmission experiments using different observational products.Similar conclusions are reached when using other temperature or precipitation datasets.Consistent with previous studies[21; 22], parameterised convection favours the occurrence of light rainfall (FigS2a-b, S2d-e, and S3a).However, even with more frequent light rainfall days in R25 h compared to CP4 h , errors in 10-day precipitation accumulations are greater in CP4 h particularly over high-altitude regions such as the East African highlands and Mount Cameroon (Fig S2g,h).For example, the RMSD in 10-day precipitation accumulations is 1.64 mm greater in CP4 h than R25 h .